Question

find the sum of first 20 terms of arithmetic progression with a = 1 and 20th term l = 58​

Answer 1

Answer:

590

Step-by-step explanation:

Given that,

First Term, a = 1

a₂₀ = 58

20th term, a₂₀ = a + 19d  ---- since aₙ = a + (n - 1)d

a + 19d = 58

1 + 19d = 58

19d = 58-1

19d = 57

d = 57/19

d = 3

Sum to n terms,

Sₙ = $\frac{n}{2} (a+an)$

Sₙ = $\frac{20}{2}(1+58) \\= 10 * 59\\= 590$

Answer 2

$\bf\purple{QuestioN:-}$

Find the sum of first 20 terms of arithmetic progression when a = 1 and 20th term = 58​.

$\bf\pink{AnsweR:-}$

$\underline{\underline{\rm{\bigstar\:Given\::-}}}$

• No. of terms = 20

• First term = 1

• Last term = 58

$\underline{\underline{\rm{\bigstar\:To\:Find\::-}}}$

• The sum of first 20 terms of the AP

$\underline{\underline{\rm{\bigstar\:Solution\::-}}}$

Formula that can be applied here is,

$\implies\bf{S_n=\dfrac{n}{2}\times(First\:term+\:last\:term)}$

On substituting values,

$\implies\bf{S_{20}=\dfrac{20}{2}\times(1+58)}$

$\implies\bf{S_{20}=10\times59}$

$\implies\bf{S_{20}=590}$

Hence,

The sum of first 20 terms of this AP is 590.

The required answer for your question is 590.

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